Hey Eagle,
Did the tweets have full aerobatic capabililty or was it limited? Just curious.
Full aerobatic, stressed to positive 6.67 and negative 2.5 (if I recall correctly... maybe it was neg 4, can't remember). We added a prohibition against intentional negative-G flight due to the age of the oil system and potential for temporarily starving the engine of oil, and snap rolls were prohibited due to the violence of the maneuver depending on entry speed. But otherwise fully aerobatic and incredibly predictable.
I think the negative G flight limit was 30 seconds because that's how much fuel the inverted reservoir would hold.
I was doing a little "follow the leader" maneuvering against another IP in a second T-37 (technically it was our "extended trail" exercise but we flew more aggressively when it was just instructors in the planes) and at one point, I found myself inverted with very low airspeed and with the other guy about 1000 ft behind me. Knowing that our flight paths could not intersect due to the geometry of the situation, I thought I'd give him a little suprise. I gently pulled the plane almost into the stall (an experienced pilot can feel this by varying amounts of airframe buffeting) and nudged just a tiny bit of rudder to get the nose rotating. I let the plane rotate 180 degrees and halted the rotation by easing off on the stick and applying opposite rudder, still inverted and doing only about 60 knots. It wasn't a tail slide or anything prohibited, but because of the geometry of the maneuver I was inverted, still climbing with positive G's, with essentially no forward airspeed and drifting away from the other plane, but I was pointed right at him. It shocked him so much that since he was also very near the stall, his instinctive twitch on the controls sent him into an impending spin entry. Since I was still fully under control, I was able to flop right down onto his 6 as he fluttered on past. Of course that sort of position change isn't allowed under the "extended trail" exercise, so we knocked it off and set up another exercise

Good clean fun, within the rules/regulations, something we did to improve our mastery of the plane and make us better instructors.
My point is that the plane was a joy to fly especially once you figured out exactly how much the plane would give you and where it would bite you in the butt. We taught the students to fly in the center of the envelope and how to recover back to the center if they went out of control, but as instructors we could go out and explore the WHOLE envelope because the plane was so durable and forgiving. The T-6, not so much... If you try to do that with a T-6 the prop would probably fall off or something else yet equally disastrous would happen.